OMPhQuiz_08_p67-75 - chapter 8 Conservation of Energy...

Potential energy of a conservative force (Section 8.1)1. Mass–spring system• Context in the textbook: Before Example 1 in Section 8.1.2. Conservative force: Path integrals• Context in the textbook: Section 2.1 considers conservative force in onedimension. This example verifies the path-independent property of aconservative force in two dimensions. It may be used at the end of Section8.1.Potential energy due to gravity plus spring force (Section 8.2)The following exercises may be used before Example 4 in Section 8.2:3. Spring toy: Maximum height4. Spring toy: Special points of U5. Releasing a compressed spring6. Spring–pulley system with frictionPower (Section 8.5)Two exercises before Example 9 of Section 8.5:7. Climbing up a hill8. Maximum speed on a flat roadContentsPhysiQuiz67chapter8Conservation of Energy

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Consider a mass–spring system. The spring force asserted on the block isgiven by Hooke’s Law: Fspringk x. Denote the potential energy of thespring by U(x). At x0 the spring is relaxed: U(0)0. U(x) is the workdone by the stretching force in going from xO to xx, which is givenby which of the following?ABCDkx2kx2x0kxdxx0kxdxExtra:Release the mass from rest at xx. Determine the kinetic energy atx0 in terms of x, k, m. Hint:Not all the quantities here need to be used.Explanation: When the spring is pulled to the right, both the pulling forceand the displacement are in the same direction. The pulling force is oppositeto the spring force. The latter obeys Hooke’s Law: FpullFspringk x. Sowork done in stretching the spring from xO to xxis given by Answer C.

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